A projectile is fired in such a way that its horizontal range is equal to 13.5 times its maximum height. What is the angle of projection?

Maximum height: h = v0² sin² α / 2 g

Horizontal range: x = v0² sin 2 α / g

13.5 v0² sin² α / 2 g = v0² sin 2 α / g / : v0²/g

6.75 sin² α = 2 sin α cos α / : sin α

6.75 sin α = 2 cos α / : cos α

6.75 tan α = 2

tan α = 0.2963

α = tan^ (-1) 0.2963

α = 16.504° ≈ 16.5°

The angle of projection is 16° 30'.